I don't have a problem with it ethically for criminals who are guilty of horrendous crimes as long as they get the full and fair due process, which is quite lengthy and expensives.
However, as a practical matter, I don't think it works to well. It's been shown to not be a deterant. It costs more and ties up more of the legal system. Plus, the stress it places on the jury can cause problems like we just saw in the Jodi Arias trial.
So, ethically, it's all right in some cases but practically not really worthwhile.